Base

`BaseCopula`

BaseCopula(
    kendall_tau: float,
    rotation: str | systematica.models.arbitrage_index.utils.BaseCopulaRotation = BaseCopulaRotation.R0,
    start: float = 0.001,
    stop: float = 0.999,
    num: int = 100,
)

Abstract base class for copula models used for statistical arbitrage and copula-based modeling. Method generated by attrs for class BaseCopula.

Ancestors

abc.ABC

Descendants

systematica.models.arbitrage_index.clayton.Clayton
systematica.models.arbitrage_index.frank.Frank
systematica.models.arbitrage_index.gumbel.Gumbel
systematica.models.arbitrage_index.joe.Joe
systematica.models.arbitrage_index.student_t.StudentT

Instance variables

model_name: str: Model name, incl. fitted rotation
dependence: float: Estimate the parameters from copulas and the Kendall rank correlation.
lower_tail_dependence: float: Theoretical lower tail dependence coefficient.
upper_tail_dependence: float: Theoretical upper tail dependence coefficient.
kendall_tau: float: Kendall’s tau correlation coefficient, with values ranging from -1 (perfect disagreement) to 1 (perfect agreement) and 0 indicating no correlation.
linear_space: numpy.ndarray:
num: int: Number of samples to generate. Must be at least 10. Default is 100.
rotation: str | systematica.models.arbitrage_index.utils.BaseCopulaRotation: Rotations allow the copula to be adapted for different types of tail dependence. - A 180 rotation captures extreme co-movements in the lower tail (i.e. simultaneous extreme losses). - A 90 rotation captures scenarios where one variable exhibits extreme losses while the other shows extreme gains. - A 270 rotation captures the opposite scenario, where one variable experiences extreme gains while the other suffers extreme losses. See BaseCopulaRotation. If set to auto, applies best fitted rotation. Defaults to BaseCopulaRotation.R0.
rotation_: systematica.models.arbitrage_index.utils.BaseCopulaRotation: Best fitted rotation applied to the copula model, initialized to R0 (no rotation).
sample: Tuple[numpy.ndarray, numpy.ndarray]:
start: float: The starting value of the sequence. Must be greater than 0. Defaults to 0.001.
stop: float: The end value of the sequence. Must be less than 1. Defaults to 0.999.

Methods

`density`

density(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
) ‑> numpy.ndarray

Estimate the log probability density function for given ui and vi values. Parameters:

Name	Type	Default	Description
`u`	`tp.Array1d`	`--`	First uniform marginal.
`v`	`tp.Array1d`	`--`	Second uniform marginal.

Returns:

Type	Description
`tp.Array1d`	Log probability density.

`cumulative_density`

cumulative_density(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
) ‑> numpy.ndarray

Calculate cumulative density of the bivariate copula:

P(U<=u, V<=v)

Parameters:

Name	Type	Default	Description
`u`	`tp.Array1d`	`--`	First uniform marginal.
`v`	`tp.Array1d`	`--`	Second uniform marginal.

Returns:

Type	Description
`tp.Array1d`	Cumulative probability density.

`arbitrage`

arbitrage(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
) ‑> numpy.ndarray

Calculate the mispricing index for every time step in the trading period using the estimated copula. Mispricing indices are the conditional probabilities:

P(U < u | V = v) \text{ and } P(V < v | U = u).

Parameters:

Name	Type	Default	Description
`u`	`tp.Array1d`	`--`	The first component of the bivariate input.
`v`	`tp.Array1d`	`--`	The second component of the bivariate input.

Returns:

Type	Description
`tp.Array2d`	The mispricing indices for the copula, a.k.a. arbitrage.

`partial_derivative`

partial_derivative(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
) ‑> numpy.ndarray

Compute the h-function (partial derivative) for the bivariate copula, a.k.a. the mispricing index, for every time step in the trading period using the estimated copula. Parameters:

Name	Type	Default	Description
`u`	`tp.Array1d`	`--`	The first component of the bivariate input.
`v`	`tp.Array1d`	`--`	The second component of the bivariate input.

Returns:

Type	Description
`tp.Array2d`	The mispricing indices for the copula, a.k.a. arbitrage.

`score`

score(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
) ‑> numpy.ndarray

Compute the log-likelihood score of each sample (log-pdf) under the model.

u and v are bivariate inputs (u, v) where each row represents a bivariate observation. Both u and v must be in the interval [0, 1], having been transformed to uniform marginals.

Parameters:

Name	Type	Default	Description
`u`	`tp.Array1d`	`--`	The first component of the bivariate input.
`v`	`tp.Array1d`	`--`	The second component of the bivariate input.

Returns:

Type	Description
`tp.Array1d`	The log-likelihood score of each sample under the fitted copula.

`probability`

probability(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
) ‑> numpy.ndarray

Probability density function (PDF).

u and v are bivariate inputs (u, v) where each row represents a bivariate observation. Both u and v must be in the interval [0, 1], having been transformed to uniform marginals.

Returns:

Type	Description
`tp.Array2d`	Probability density function (PDF).

`set_rotation`

set_rotation(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
) ‑> Self

Set rotation. Parameters:

Name	Type	Default	Description
`u`	`tp.Array1d`	`--`	First uniform marginal.
`v`	`tp.Array1d`	`--`	Second uniform marginal.

Returns:

Type	Description
`tp.Self`	Copula instance

`best_fit`

best_fit(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
) ‑> Tuple[numpy.ndarray, numpy.ndarray]

Transform u and v with rotated functions. Handle model fitting and rotation of uniform marginals. Parameters:

Name	Type	Default	Description
`u`	`tp.Array1d`	`--`	First uniform marginal.
`v`	`tp.Array1d`	`--`	Second uniform marginal.

Returns:

Type	Description
`tp.Tuple[tp.Array1d, tp.Array1d]`	Rotated marginals.

`criterion`

criterion(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
    model_validation_method: str = 'aic',
) ‑> float

Calculate the criterion value (e.g., aic) for the given copula model. Parameters:

Name	Type	Default	Description
`u`	`Array1d`	`--`	The array of the first component values.
`v`	`Array1d`	`--`	The array of the second component values.
`model_validation_method`	`str`	`aic`	The method to use for the criterion calculation. Defaults to “aic”.

Returns:

Type	Description
`float`	The criterion value for the model, or NaN if score cannot be computed.

Raises:

Type	Description
`ValueError`	If the provided method is not supported.

`tail_concentration`

tail_concentration(
    self,
    u_or_v: numpy.ndarray,
) ‑> numpy.ndarray

Compute the tail concentration function for a set of quantiles. The tail concentration function is defined as follows:

For quantiles $q ≤ 0.5$ : $C(q) = P(U ≤ q, V ≤ q) / q$
For quantiles $q > 0.5$ : $C(q) = (1 - 2q + P(U ≤ q, V ≤ q)) / (1 - q)$

where

U

and

V

are the pseudo-observations of the first and second variables, respectively. This function returns the concentration values for each

q

provided. References:

“Quantitative Risk Management: Concepts, Techniques, and Tools”, McNeil, Frey, Embrechts (2005)

Parameters:

Name	Type	Default	Description
`u_or_v`	`tp.Array1d`	`--`	A 1D array of quantile levels (values between 0 and 1) at which to compute the tail concentration.

Raises:

Type	Description
`ValueError`	If any value in `quantiles` is not in the interval `[0, 1]`.

Returns:

Type	Description
`tp.Array1d`	The computed tail concentration values corresponding to each quantile.

`empirical_tail_concentration`

empirical_tail_concentration(
    self,
    u: numpy.ndarray,
    v: numpy.ndarray,
    quantiles: numpy.ndarray,
) ‑> numpy.ndarray

Compute empirical tail concentration for the two variables in X. This function computes the concentration at each quantile provided. The tail concentration are estimated as:

Lower tail:

\lambda_L(q) = P(U_2 ≤ q | U_1 ≤ q)

Upper tail:

\lambda_U(q) = P(U_2 ≥ q | U_1 ≥ q)

where

U_1

and

U_2

are the pseudo-observations. Parameters:

Name	Type	Default	Description
`u`	`tp.Array1d`	`--`	The array of the first component values.
`v`	`tp.Array1d`	`--`	The array of the second component values.
`quantiles`	`tp.Array1d`	`--`	A 1D array of quantile levels (values between 0 and 1) at which to compute the concentration.

Raises:

Type	Description
`ValueError`	If `X` is not a 2D array with exactly 2 columns or if quantiles are not in `[0, 1]`.

Returns:

Type	Description
`tp.Array1d`	An array of empirical tail concentration values for the given quantiles.

`probability_density_matrix`

probability_density_matrix(
    self,
    to_numpy: bool = True,
) ‑> pandas.core.frame.DataFrame | numpy.ndarray

Create probability density matrix. Parameters:

Name	Type	Default	Description
`to_numpy`	`bool`	`s`	to `True` Return `numpy` array if `True`. `pandas.DataFrame` otherwise. The default is `True`.

Returns:

Type	Description
`tp.Array \| pd.DataFrame`	Probability density matrix.

`partial_derivative_matrix`

partial_derivative_matrix(
    self,
    to_numpy: bool = True,
) ‑> pandas.core.frame.DataFrame | numpy.ndarray

Create partial derivative matrix. Parameters:

Name	Type	Default	Description
`to_numpy`	`bool`	`s`	to `True` Return `numpy` array if `True`. `pandas.DataFrame` otherwise. The default is `True`.

Returns:

Type	Description
`tp.Array \| pd.DataFrame`	Probability density matrix.

`get_cross_tail_quantile_mask`

get_cross_tail_quantile_mask(
    self,
    alpha: float = 0.9,
    truncate: float = 0.5,
    to_numpy: bool = True,
) ‑> pandas.core.frame.DataFrame | numpy.ndarray

Create a boolean mask to focus on tail regions of a probability density distribution. Compute the q-th quantile of the data. Masks values in 1 - alpha quantile range of the PDF values. See np.quantile for more information.

u and v are bivariate inputs (u, v) where each row represents a bivariate observation. In this context, u and v are evenly spaced numbers over [start, stop, num] interval.

Parameters:

Name	Type	Default	Description
`alpha`	`float`	`s`	to `0.9` Lower quantile is found with `lower_quantile = np.quantile(pdfs, 1.0 - alpha)`, then removed from matrix. Defaults to `0.9`.
`truncate`	`float`	`s`	to `0.5` Truncate filter at specific point. Ignored if None. Defaults to `0.5`.
`to_numpy`	`bool`	`s`	to `True` Return `numpy` array if `True`. `pandas.DataFrame` otherwise. The default is `True`.

Returns:

Type	Description
`tp.Array2d \| pd.DataFrame`	Boolean array of same shape as `matrix`.

`get_cross_tail_triangle_mask`

get_cross_tail_triangle_mask(
    self,
    lower_triangle: float = 0.5,
    upper_triangle: float = 0.5,
    to_numpy: bool = True,
) ‑> pandas.core.frame.DataFrame | numpy.ndarray

Create a boolean mask to focus on triangle regions of a probability density distribution.

u and v are bivariate inputs (u, v) where each row represents a bivariate observation. In this context, u and v are evenly spaced numbers over [start, stop, num] interval.

Parameters:

Name	Type	Default	Description
`lower_triangle`	`float`	`s`	to `0.5` Lower triangle coordinate point. Defaults to `0.5`.
`upper_triangle`	`float`	`s`	to `0.5` Upper triangle coordinate point. Defaults to `0.5`.
`to_numpy`	`bool`	`s`	to `True` Return `numpy` array if `True`. `pandas.DataFrame` otherwise. The default is `True`.

Returns:

Type	Description
`tp.Array2d \| pd.DataFrame`	Boolean array of same shape as `matrix`.

`cross_tail_mask`

cross_tail_mask(
    self,
    mask_method: str = 'quantile',
    features: numpy.ndarray = None,
    **mask_method_kwargs,
) ‑> vectorbtpro.utils.figure.FigureWidget

Get cross-tail concentration mask. Parameters:

Name	Type	Default	Description
`mask_method`	`str`	`--`	Type of mask to apply to the matrix. Options are: - ‘quantile’: Apply a quantile-based tail mask. - ‘triangle’: Apply a triangular mask. Defaults to `quantile`.
`features`	`tp.Array2d`	`s`	to `None`. The array of the component values. Find linear space in the index array that correspond to adjusted values, then clip space to ensure they stay within bounds and apply mask only to valid indices. Useful to apply mask to array of ranked vectors. Defaults to `None`.
`mask_method_kwargs`	`tp.Kwargs`	`--`	Tail mask key-word arguments.

Returns:

Type	Description
`tp.Array2d \| pd.DataFrame`	Boolean array of same shape as `matrix`.

`apply_cross_tail_concentration`

apply_cross_tail_concentration(
    self,
    features: numpy.ndarray,
    mask_method: str = 'quantile',
    **mask_method_kwargs,
) ‑> vectorbtpro.utils.figure.FigureWidget

Apply cross-tail concentration mask. Parameters:

Name	Type	Default	Description
`features`	`tp.Array2d`	`--`	The array of the component values.
`mask_method`	`str`	`--`	Type of mask to apply to the matrix. Options are: - ‘quantile’: Apply a quantile-based tail mask. - ‘triangle’: Apply a triangular mask. Defaults to `quantile`.
`mask_method_kwargs`	`tp.Kwargs`	`--`	Mask key-word arguments.

Returns:

Type	Description
`tp.Array2d \| pd.DataFrame`	Filtered scaled data array.

`plot_tail_concentration`

plot_tail_concentration(
    self,
    u: numpy.ndarray = None,
    v: numpy.ndarray = None,
    title: str | None = None,
    smoothing: float | None = 1.3,
) ‑> vectorbtpro.utils.figure.Figure

Plot the tail concentration function. This method computes the tail concentration function at 100 evenly spaced quantile levels between 0.005 and 0.995. The plot displays the concentration values on the y-axis and the quantile levels on the x-axis. The tail concentration are estimated as:

Lower tail:

\delta_L(q) = P(U_2 ≤ q | U_1 ≤ q)

Upper tail:

\delta_U(q) = P(U_2 ≥ q | U_1 ≥ q)

where

U_1

and

U_2

are the pseudo-observations of the first and second variables, respectively. Parameters:

Name	Type	Default	Description
`u`	`Array1d`	`--`	The array of the first component values. If provided, it is used to plot the empirical tail concentration for comparison versus the model tail concentration.
`v`	`Array1d`	`--`	The array of the second component values. If provided, it is used to plot the empirical tail concentration for comparison versus the model tail concentration.
`title`	`str`	`None`	The title for the plot. If not provided, a default title based on the fitted copula’s representation is used.
`smoothing`	`float`	`1.3`	Smoothing parameter for the spline line shape. If provided, the curves will be smoothed using a spline interpolation.

Returns:

Type	Description
`fig : go.Figure`	A Plotly figure object containing the tail concentration curve.

`plot_ecdf`

plot_ecdf(
    self,
    u: <built-in function array>,
    v: <built-in function array>,
    **layout_kwargs,
) ‑> vectorbtpro.utils.figure.FigureWidget

Plot the empirical cumulative distribution function (ECDF) surface. Parameters:

Name	Type	Default	Description
`u`	`np.array`	`--`	The array of the first component values.
`v`	`np.array`	`--`	The array of the second component values.
`layout_kwargs`	`tp.Kwargs`	`--`	Additional arguments passed to the scatter plot.

Returns:

Type	Description
`vbt.FigureWidget`	The figure containing the scatter plot of the ECDF.

`plot_heatmap`

plot_heatmap(
    self,
    title: str | None = None,
    fig: plotly.basedatatypes.BaseFigure = None,
    **layout_kwargs,
) ‑> vectorbtpro.utils.figure.Figure

Plot a 2D heatmap contour of the estimated probability density function (PDF). This method generates a grid over [0, 1]^2, computes the PDF, and displays a contour plot of the PDF. Contour levels are limited to the 97th quantile to avoid extreme densities. Parameters:

Name	Type	Default	Description
`title`	`str`	`None`	The title for the plot. If not provided, a default title based on the fitted copula’s representation is used.
`fig`	`tp.BaseFigure`	`None`	Existing figure to update. If None, a new figure is created. Defaults to `None`.
`layout_kwargs`	`tp.Kwargs`	`--`	Additional keyword arguments for customizing the layout.

Returns:

Type	Description
`fig : go.Figure`	A Plotly figure object containing the 2D contour plot of the PDF.

`plot_surface`

plot_surface(
    self,
    title: str | None = None,
    fig: plotly.basedatatypes.BaseFigure = None,
    **layout_kwargs,
) ‑> plotly.graph_objs._figure.Figure

Plot a 3D surface of the estimated probability density function (PDF). This method generates a grid over [0, 1]^2, computes the PDF, and displays a 3D surface plot of the PDF using Plotly. Parameters:

Name	Type	Default	Description
`title`	`str`	`None`	The title for the plot. If not provided, a default title based on the fitted copula’s representation is used.
`fig`	`tp.BaseFigure`	`None`	Existing figure to update. If None, a new figure is created. Defaults to `None`.
`layout_kwargs`	`tp.Kwargs`	`--`	Additional keyword arguments for customizing the layout.

Returns:

Type	Description
`fig : go.Figure`	A Plotly figure object containing a 3D surface plot of the PDF.

`plot_contour`

plot_contour(
    self,
    u: numpy.ndarray | pandas.core.series.Series | pandas.core.frame.DataFrame = None,
    v: numpy.ndarray | pandas.core.series.Series | pandas.core.frame.DataFrame = None,
    signals: systematica.signals.base.Signals | pandas.core.frame.DataFrame = None,
    select_signals: str = None,
    show_contour: bool = True,
    show_data: bool = True,
    show_latest_point: bool = False,
    show_points: Dict[str, int | pandas._libs.tslibs.timestamps.Timestamp] = None,
    mask_array: numpy.ndarray = None,
    alpha: float = 0.5,
    opacity: float = 0.2,
    title: str | None = None,
    showlegend: bool = True,
    fig: plotly.basedatatypes.BaseFigure = None,
    **layout_kwargs,
) ‑> vectorbtpro.utils.figure.Figure

Name	Type	Default	Description
`u`	`np.array`	`None`	The array of the first component values. Ignored it `None`. Defaults to `None`.
`v`	`np.array`	`--`	The array of the second component values. Ignored it `None`. Defaults to `None`.
`signals`	`Signals`	`None`	Signal namedtuple object. Array should be the same size as `u` and `v`.
`select_signals`	`tp.Literal[VALID_SIGNALS]`	`None`	Filter `Signals` by a signal (e.g. `long_entries`). If None, It is ignored. Defaults to `None`.
`show_contour`	`bool`	`True`	Show contour if `True`. Defaults to `True`.
`show_data`	`bool`	`True`	If `True`, display selected data. Defaults to `True`.
`show_latest_point`	`bool, Default` True“	`--`	If True, show latest values as red dot. Defaults to True.
`show_points`	`tp.Dict[str, int \| pd.Timestamp], Default` None“	`--`	Show selected color and values mapping. Ignored if None. Defauts to None.
`mask_array`	`tp.Array2d`	`--`	Boolean mask to focus on specific regions of a probability density distribution. Applied to `u` and `v`. Defaults to None.
`alpha`	`float`	`0.5`	Contour alpha size. Defaults to `0.5`.
`opacity`	`float`	`0.2`	Point opacity. Defaults to `0.2`.
`title`	`str`	`None`	The title for the plot. If not provided, a default title based on the fitted copula’s representation is used.
`showlegend`	`bool`	`True`	Show legend. Defaults to `True`.
`fig`	`tp.BaseFigure`	`None`	Existing figure to update. If None, a new figure is created. Defaults to `None`.
`layout_kwargs`	`tp.Kwargs`	`--`	Additional keyword arguments for customizing the layout.

Returns:

Type	Description
`fig : go.Figure`	A Plotly figure object containing the 2D contour plot of the PDF.

`plot_ellipse`

plot_ellipse(
    self,
    u: numpy.ndarray | pandas.core.series.Series | pandas.core.frame.DataFrame,
    v: numpy.ndarray | pandas.core.series.Series | pandas.core.frame.DataFrame,
    std: float | List[float] = None,
    show_data: bool = True,
    opacity: float = 0.2,
    title: str | None = None,
    showlegend: bool = True,
    fig: plotly.basedatatypes.BaseFigure = None,
    **layout_kwargs,
) ‑> vectorbtpro.utils.figure.Figure

Plot an ellipse based on the covariance matrix of a 2D dataset. Parameters:

Name	Type	Default	Description
`arr`	`tp.Array2d`	`--`	Input data of shape (n_samples, 2) representing the 2D points.
`std`	`float`	`2.0`	Standard deviation threshold(s) defining the size of the ellipse (e.g., 2 for ~95% confidence). If None, threshold are 0.5, 1, 1.5 std from the mean. Defaults to None.
`show_data`	`bool`	`True`	If `True`, display selected data. Defaults to `True`.
`opacity`	`float`	`0.2`	Point opacity. Defaults to `0.2`.
`title`	`str`	`None`	The title for the plot. If not provided, a default title based on the fitted copula’s representation is used.
`showlegend`	`bool`	`True`	Show legend. Defaults to `True`.
`fig`	`tp.BaseFigure`	`None`	Existing figure to update. If None, a new figure is created. Defaults to `None`.
`layout_kwargs`	`tp.Kwargs`	`--`	Additional keyword arguments for customizing the layout.

Returns:

Type	Description
`vbt.FigureWidget`	Scatter plot with ellipse.

`plot_density`

plot_density(
    self,
    mask_method: Literal['qth', 'tri', None] = None,
    mask_method_kwargs: Dict[str, Any] = None,
    features: numpy.ndarray = None,
    opacity: float = 0.8,
    title: str | None = None,
    showlegend: bool = True,
    fig: plotly.basedatatypes.BaseFigure = None,
    **layout_kwargs,
) ‑> vectorbtpro.utils.figure.FigureWidget

Plot probability density matrix. Parameters:

Name	Type	Default	Description
`mask_method`	`str`	`--`	Type of mask to apply to the matrix. Options are: - ‘qth’: Apply a quantile-based tail mask. - ‘tri’: Apply a triangular mask. - `None`: No mask applied. Defaults to None.
`mask_method_kwargs`	`tp.Kwargs`	`--`	Additional keyword arguments passed to the mask functions.
`features`	`tp.Array2d`	`--`	Input data of shape (n_samples, 2) representing the 2D points.
`opacity`	`float`	`0.8`	Point opacity. Defaults to `0.8`.
`title`	`str`	`None`	The title for the plot. If not provided, a default title based on the fitted copula’s representation is used.
`showlegend`	`bool`	`True`	Show legend. Defaults to `True`.
`fig`	`tp.BaseFigure`	`None`	Existing figure to update. If None, a new figure is created. Defaults to `None`.
`layout_kwargs`	`tp.Kwargs`	`--`	Additional keyword arguments for customizing the layout.

Returns:

Type	Description
`vbt.FigureWidget`	Matrix plot.

Raises:

Type	Description
`RuntimeError:`	Failed to generate heatmap

Overview

Arbitrage Index

Meta Model

Momentum

Ou Process

Range Breakout

Volatility

Volume Profile

`BaseCopula`

Ancestors

Descendants

Instance variables

Methods

`density`

`cumulative_density`

`arbitrage`

`partial_derivative`

`score`

`probability`

`set_rotation`

`best_fit`

`criterion`

`tail_concentration`

`empirical_tail_concentration`

`probability_density_matrix`

`partial_derivative_matrix`

`get_cross_tail_quantile_mask`

`get_cross_tail_triangle_mask`

`cross_tail_mask`

`apply_cross_tail_concentration`

`plot_tail_concentration`

`plot_ecdf`

`plot_heatmap`

`plot_surface`

`plot_contour`

`plot_ellipse`

`plot_density`

Overview

Arbitrage Index

Meta Model

Momentum

Ou Process

Range Breakout

Volatility

Volume Profile

​BaseCopula

​Ancestors

​Descendants

​Instance variables

​Methods

​density

​cumulative_density

​arbitrage

​partial_derivative

​score

​probability

​set_rotation

​best_fit

​criterion

​tail_concentration

​empirical_tail_concentration

​probability_density_matrix

​partial_derivative_matrix

​get_cross_tail_quantile_mask

​get_cross_tail_triangle_mask

​cross_tail_mask

​apply_cross_tail_concentration

​plot_tail_concentration

​plot_ecdf

​plot_heatmap

​plot_surface

​plot_contour

​plot_ellipse

​plot_density

`BaseCopula`

Ancestors

Descendants

Instance variables

Methods

`density`

`cumulative_density`

`arbitrage`

`partial_derivative`

`score`

`probability`

`set_rotation`

`best_fit`

`criterion`

`tail_concentration`

`empirical_tail_concentration`

`probability_density_matrix`

`partial_derivative_matrix`

`get_cross_tail_quantile_mask`

`get_cross_tail_triangle_mask`

`cross_tail_mask`

`apply_cross_tail_concentration`

`plot_tail_concentration`

`plot_ecdf`

`plot_heatmap`

`plot_surface`

`plot_contour`

`plot_ellipse`

`plot_density`